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引用次数: 0
摘要
我们在之前的论文(Hanson in Math Logic Q 69(4):482 - 507,2023)中介绍的畸变系统的背景下探索近似范畴,畸变系统是Yaacov (J Math Logic 08(02): 225-249, 2008)引入的微扰系统的温和推广。我们将Ben Yaacov关于可分离近似范畴理论的Ryll-Nardzewski风格刻画从摄动系统推广到畸变系统。我们也在不可分近似范畴的Morley定理的类比方面取得了进展,表明如果存在一些不可数基数\(\kappa \)使得每个大小模型\(\kappa \)在适当的意义上都是“近似饱和的”,那么对于所有不可数基数也是如此。最后,我们给出了这些现象的一些例子,并强调了普通可分范畴和不可分近似范畴之间的明显相互作用。
We explore approximate categoricity in the context of distortion systems, introduced in our previous paper (Hanson in Math Logic Q 69(4):482–507, 2023), which are a mild generalization of perturbation systems, introduced by Yaacov (J Math Logic 08(02):225–249, 2008). We extend Ben Yaacov’s Ryll-Nardzewski style characterization of separably approximately categorical theories from the context of perturbation systems to that of distortion systems. We also make progress towards an analog of Morley’s theorem for inseparable approximate categoricity, showing that if there is some uncountable cardinal \(\kappa \) such that every model of size \(\kappa \) is ‘approximately saturated,’ in the appropriate sense, then the same is true for all uncountable cardinalities. Finally we present some examples of these phenomena and highlight an apparent interaction between ordinary separable categoricity and inseparable approximate categoricity.
期刊介绍:
The journal publishes research papers and occasionally surveys or expositions on mathematical logic. Contributions are also welcomed from other related areas, such as theoretical computer science or philosophy, as long as the methods of mathematical logic play a significant role. The journal therefore addresses logicians and mathematicians, computer scientists, and philosophers who are interested in the applications of mathematical logic in their own field, as well as its interactions with other areas of research.